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\section{\module{cmath} ---
Mathematical functions for complex numbers}
\declaremodule{builtin}{cmath}
\modulesynopsis{Mathematical functions for complex numbers.}
This module is always available. It provides access to mathematical
functions for complex numbers. The functions are:
\begin{funcdesc}{acos}{x}
Return the arc cosine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{acosh}{x}
Return the hyperbolic arc cosine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{asin}{x}
Return the arc sine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{asinh}{x}
Return the hyperbolic arc sine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{atan}{x}
Return the arc tangent of \var{x}.
\end{funcdesc}
\begin{funcdesc}{atanh}{x}
Return the hyperbolic arc tangent of \var{x}.
\end{funcdesc}
\begin{funcdesc}{cos}{x}
Return the cosine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{cosh}{x}
Return the hyperbolic cosine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{exp}{x}
Return the exponential value \code{e**\var{x}}.
\end{funcdesc}
\begin{funcdesc}{log}{x}
Return the natural logarithm of \var{x}.
\end{funcdesc}
\begin{funcdesc}{log10}{x}
Return the base-10 logarithm of \var{x}.
\end{funcdesc}
\begin{funcdesc}{sin}{x}
Return the sine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{sinh}{x}
Return the hyperbolic sine of \var{x}.
\end{funcdesc}
\begin{funcdesc}{sqrt}{x}
Return the square root of \var{x}.
\end{funcdesc}
\begin{funcdesc}{tan}{x}
Return the tangent of \var{x}.
\end{funcdesc}
\begin{funcdesc}{tanh}{x}
Return the hyperbolic tangent of \var{x}.
\end{funcdesc}
The module also defines two mathematical constants:
\begin{datadesc}{pi}
The mathematical constant \emph{pi}, as a real.
\end{datadesc}
\begin{datadesc}{e}
The mathematical constant \emph{e}, as a real.
\end{datadesc}
Note that the selection of functions is similar, but not identical, to
that in module \refmodule{math}\refbimodindex{math}. The reason for having
two modules is that some users aren't interested in complex numbers,
and perhaps don't even know what they are. They would rather have
\code{math.sqrt(-1)} raise an exception than return a complex number.
Also note that the functions defined in \module{cmath} always return a
complex number, even if the answer can be expressed as a real number
(in which case the complex number has an imaginary part of zero).
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